IPMAT Indore (MCQ) PYQs

200%

2%

4%

400%

6

7

8

9

1

2

3

4

96

78

42

54

$20 ≤ x ≤ 50$

$x ≤ 20$

$x ≥ 50$

$10 ≤ x ≤ 70$

7

8

10

12

3

1

2

No real values of x satisfies the inequality

[-1,2]

[-$\frac{1}{2}$, 2]

[-1,1]

[-$\frac{1}{2}$, 1]

$x \in \left( \frac{1}{3}, 1 \right)$

$x \in \left( \frac{1}{3}, 2 \right)$

$x \in \left( 0, \frac{1}{3} \right) \cup \left( 1, 2 \right)$

$x \in \left( -\infty, 1 \right)$

$\left( \frac{1}{2}, 1 \right)$

$\left( \frac{1}{2}, \infty \right)$

$\left( -\infty, \frac{1}{2} \right)$

$\left( -\infty, \frac{1}{2} \right) \cup \left( 1, \infty \right)$

$2 + \sqrt{3}$

$1 + \sqrt{2}$

$7 + 4\sqrt{3}$

$97 + 56\sqrt{3}$

$1 : (1 + n)$

$1 : n$

$1 + n^2 : (1 + n)^2$

$(1 + n) : (1 + n^2)$

$\frac{\sqrt{15} + \sqrt{35}}{2}$ m

$8$ m

$\sqrt{13}$ m

$6$ m

12 square units

3 square units

4 square units

24 square units

the cow moves in a straight line

the cow moves in a circle

the cow moves in a parabola

the cow moves in a hyperbola

$[-1, 1]$

$[-2, 2]$

$[0, \sqrt{3}]$

$[-\sqrt{3}, \sqrt{3}]$

$\frac{3(m^2+1)}{4}$

$\frac{3(m^2-1)}{4}$

$1-\frac{3(m^2-1)}{4}$

$1-\frac{3(m^2-1)^2}{4}$

$0.5$

$1$

$2$

$3$

positive and monotonically increasing for x $\in (-\infty, \frac{5-\sqrt{57}}{2})$ and x $\in (\frac{5+\sqrt{57}}{2}, +\infty)$

negative and monotonically decreasing for x $\in (-\infty, \frac{5-\sqrt{57}}{2})$ and x $\in (\frac{5+\sqrt{57}}{2},+\infty)$

negative and monotonically increasing for x $\in (-\infty, \frac{5-\sqrt{57}}{2})$ and positive and monotonically increasing for x $\in (\frac{5+\sqrt{57}}{2},+\infty)$

positive and monotonically increasing for x $\in (-\infty, \frac{5-\sqrt{57}}{2})$ and negative and monotonically decreasing for x $\in (\frac{5+\sqrt{57}}{2},+\infty)$

$2a - b - c$

$a + b - 2c$

$a + b + c$

$a - c$

-34

30

26

-38

31

32

30

29

17

16

19

15

$f(2) = \frac{1}{13} > f(3)$

$\frac{1}{13} > f(2) > f(3)$

$f(3) > f(2) = \frac{1}{13}$

$f(2) = f(3) = \frac{1}{13}$

$\frac{1}{6}$

$\frac{1}{4}$

$\frac{1}{5}$

$\frac{1}{10}$

4

4.667

4.333

3.667

0.5

30

2

1

$f(x) > g(x) > 0$ for $0 < a < 1$ and $g(x) > f(x) > 0$ for $a > 1$

$g(x) > f(x) > 0$ for $0 < a < 1$ and $f(x) > g(x) > 0$ for $a > 1$

$f(x) > g(x) > 0$ for $a > 0$

$g(x) > f(x) > 0$ for $a > 0$

$764 \ \text{cm}^3$ and $586 \ \text{cm}^3$

$586 \ \text{cm}^3$ and $564 \ \text{cm}^3$

$764 \ \text{cm}^3$ and $564 \ \text{cm}^3$

$586 \ \text{cm}^3$ and $786 \ \text{cm}^3$

$2^{300}$

$3^{200}$

$2^{100} + 3^{100}$

$4^{100}$

435

465

450

464

$\dfrac{u}{v}$

$\dfrac{u}{v-u}$

$\dfrac{v-u}{v+u}$

$\dfrac{u}{v+u}$

$7:9$

$9:7$

$9:5$

$5:9$

64

128

190

254

$n$ is a multiple of 2 but not a multiple of 4

$n$ is a multiple of 3

$n$ can be any multiple of 4

The only possible value of $n$ is 4